Math Problem Statement

The user provided an image of a table requiring conversion of various values into scientific notation, along with identifying their order of magnitude.

Solution

The image contains a table that requires converting values into scientific notation and categorizing them by order of magnitude. Let's break it down:

Here is a quick overview of the table structure:

  • Grandezza (Quantity): Refers to the physical quantities like Earth's equatorial radius, mass of a whale, etc.
  • Valore (Value): These are the numeric values that need to be converted into scientific notation.
  • Notazione Scientifica (Scientific Notation): This is where you'll rewrite the values in the table using scientific notation.
  • Ordine di grandezza (Order of Magnitude): This refers to the closest power of 10 for the scientific notation of the values.

The columns seem to list the following dataThe image contains a table that requires converting values into scientific notation and categorizing them by order of magnitude. Let's break it down:

Here is a quick overview of the table structure:

  • Grandezza (Quantity): Refers to the physical quantities like Earth's equatorial radius, mass of a whale, etc.
  • Valore (Value): These are the numeric values that need to be converted into scientific notation.
  • Notazione Scientifica (Scientific Notation): This is where you'll rewrite the values in the table using scientific notation.
  • Ordine di grandezza (Order of Magnitude): This refers to the closest power of 10 for the scientific notation of the values.

The columns seem to list the following

  1. Raggio equatoriale della Terra (Earth's equatorial radius): 6370 km → 6.37×103km6.37 \times 10^3 \, \text{km}
  2. Altezza del monte Everest (Height of Mount Everest): 8848 m → 8.848×103m8.848 \times 10^3 \, \text{m}
  3. Velocità di una tartaruga (Speed of a turtle): 0.076 m/s → 7.6×102m/s7.6 \times 10^{-2} \, \text{m/s}
  4. Massa di una balena (Mass of a whale): 150,000 kg → 1.5×105kg1.5 \times 10^5 \, \text{kg}
  5. Diametro di una molecola di DNA (Diameter of a DNA molecule): 0.000002 m → 2×106m2 \times 10^{-6} \, \text{m}
  6. Numero di secondi in un anno (Number of seconds in a year): 31,536,000 s → 3.1536×107s3.1536 \times 10^7 \, \text{s}
  7. Numero di vocaboli conosciuti da un bambino di 5 anni (Number of words known by a 5-year-old): 3000 → 3×1033 \times 10^3
  8. Numero di alveoli nei polmoni (Number of alveoli in the lungs): 300 million → 3×1083 \times 10^8

Would you like more details on any of these conversions?

Here are some related questions:

  1. How is scientific notation helpful in representing very large or small numbers?
  2. What is the difference between scientific notation and the order of magnitude?
  3. Can the order of magnitude change depending on rounding?
  4. Why do powers of ten simplify calculations in physics and engineering?
  5. How do you convert between scientific notation and standard notation?

Tip: When converting to scientific notation, always make sure the coefficient is between 1 and 10, and adjust the exponent accordingly.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Powers of 10
Order of Magnitude

Formulas

Scientific Notation: N × 10^n where 1 ≤ N < 10
Order of Magnitude: Closest power of 10 to a number

Theorems

Powers of Ten Theorem
Scientific Notation Conversion

Suitable Grade Level

Grades 9-12